undefined | Better HN

0 pointsyongjik9y ago0 comments

1. e + ei is not real.

2. f(x) = x + sqrt(2) if there exists an integer k>=0 such that x - k * sqrt(2) is rational; f(x) = x otherwise.

This function maps all real numbers to irrational numbers, 1-to-1.

0 comments

e is real, e + ei is irrational.

I believe you mean "complex". You can form a bijection between the reals and the complex numbers by interleaving the digits, as any Google search can tell you.

Retric9y ago

For every point on your mapimg I define two points X + 1 and x + 1i. You can assign infinity to one of them but not both.

1 more reply

jakub_h9y ago

e is irrational, e+ei can't be irrational because it isn't real (all irrationals are reals).

Retric9y ago

Sorry, imaginary number composed of two irrational numbers.

j / k navigate · click thread line to collapse

0 pointsyongjik9y ago0 comments

1. e + ei is not real.

2. f(x) = x + sqrt(2) if there exists an integer k>=0 such that x - k * sqrt(2) is rational; f(x) = x otherwise.

This function maps all real numbers to irrational numbers, 1-to-1.

0 comments

Retric9y ago

e is real, e + ei is irrational.

pcmonk9y ago

I believe you mean "complex". You can form a bijection between the reals and the complex numbers by interleaving the digits, as any Google search can tell you.

Retric9y ago

For every point on your mapimg I define two points X + 1 and x + 1i. You can assign infinity to one of them but not both.

1 more reply

jakub_h9y ago

e is irrational, e+ei can't be irrational because it isn't real (all irrationals are reals).

Retric9y ago

Sorry, imaginary number composed of two irrational numbers.

j / k navigate · click thread line to collapse